# Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

## TL;DR

This paper extends previous research on a fractional order three-species food chain model by establishing the local and global stability of the interior equilibrium point, supported by numerical examples.

## Contribution

It provides the first proof of both local and global stability for the interior equilibrium in a fractional Leslie-Gower-type food chain model.

## Key findings

- Proved local stability of the interior equilibrium
- Established global stability of the interior equilibrium
- Numerical examples support analytical results

## Abstract

Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi ({\it Nonlinear Dynamics, doi: org/10.1007/s11071-018-4663-6, 2018}). They proved both the local and global asymptotic stability of all equilibrium points except the interior one. This work extends their work and gives proof of both the local and global stability analysis of the interior equilibrium point. Numerical examples are also provided to substantiate the analytical findings.